Following Yang and Yang's argument [1]} and its generalization [2]}, the GGE distribution can be described using a partition function
\(\mathcal {Z}=\int \mathcal {D}[\rho ]\exp \big (\mathcal {S}\left[\rho _{\rm p},\rho _{\rm h}[\rho _{\rm p}]\right]-w[\rho _{\rm p}]\big ) \; ,\) 
